LESSON 2LESSON 2FRACTIONSFRACTIONS

Learning OutcomesLearning OutcomesBy the end of this lesson,

students should be able to:◦Understand types of fractions.◦Convert improper fractions into

mixed numbers.◦Write a fraction in lowest terms.◦Add, subtract, multiply and divide

fractions.◦Convert decimals to fractions.◦Convert fractions to decimals.

TopicsTopicsUnderstanding the types of

fractions.◦Improper fractions and mixed

numbers.◦Writing a fraction in lowest terms.◦Adding, subtracting, multiplying and

dividing fractions.◦Converting decimals to fractions.◦Converting fractions to decimals.

Understanding the types of Understanding the types of fractionsfractionsA fraction represents part of a

whole. Fractions are written in the form of one number over another, with a line between two numbers. The line, or bar between the top number and the bottom number means “divided by”. The top number is called the numerator, and the bottom number is called the denominator.

Types of fractionsTypes of fractionsProper fraction: Numerator smaller than

denominator e.g. 2/3, ¾, 8/15 and 9/10

Improper fractionNumerator equal or greater than

denominator e.g. 5/5, 11/5, 3/2 and 9/4

Mixed fraction Whole number and proper fraction e.g.

Contd…Contd…

2

127 ,

6

54 ,

3

21

Converting fractionsConverting fractions• Mixed numbers to improper

fractions• A mixed number can be changed to an

improper fraction as follows:• Multiply the whole number by the

denominator of the fraction.• Add the numerator to that product.

The resulting sum becomes the new fraction’s numerator.

• Put that sum (the new numerator) over the original fraction’s denominator.

Example Example

3

14

3

243

3

24

Contd…Contd…Improper fractions to mixed

numbersTo convert an improper fraction to a

mixed number, divide the numerator of the improper fraction by the denominator, and place the remainder (if any) over the original denominator (the divisor).

ExampleConvert 29/5 to mixed numbers

5

45

5

29

Contd…Contd…Writing a fraction in lowest terms

If both the numerator and denominator of a fraction cannot be divided without remainder by any number other than 1, then the fraction is in lowest terms

The lowest terms for 2/4 is ½

Contd…Contd…

• Adding and subtracting fractions• Fractions with the same denominator

are called like fractions. Such fractions have a common denominator. Addition and subtraction of fractions which have a common denominator can be done by applying the operation on both numerators.

• Example • Add 3/5 and 1/5

3/5 + 1/5 = 4/5Fraction with different

denominators, are called unlike fractions. To add or subtract unlike fractions, a common denominator should be found or generated. Once a common denominator exists, apply the operation on both numerators.

Subtraction½ - 2/3

Multiplying and dividing Multiplying and dividing fractionsfractions Multiplying proper or improper

fractions

Three steps are involved when multiplying proper and improper fractions:

Multiply the numerators.Multiply the denominators.Reduce to lowest terms if

necessary.

Multiplying mixed numbersMultiplying mixed numbers

To multiply mixed numbers, first convert them into improper fractions. Then proceed as with multiplication of proper fractions.

Dividing proper or improper fractionsDividing proper or improper fractions

To divide proper or improper fractions, the followings steps should be observed:

Invert the divisor or divisors (turned upside down). The divisor is the number by which we are dividing. The inverse of a number is referred to as its reciprocal.

Proceed with multiplication.

Dividing mixed numbersDividing mixed numbers

Steps to divide mixed numbers are as follows:

Convert all mixed numbers to improper fractions.

Invert the divisor or divisors and change signs from division to multiplication.

Proceed as in multiplication

Converting decimals to Converting decimals to fractionsfractions• Decimals can be converted to fractions.

For example, 0.32 is properly read as “thirty-two hundredths”, which is the same as 32/100.

• Rules to convert decimals to fractions:• Count the digits to the right of the decimal

point. Place that many zeros in the denominator of the common fraction.

• Remove the decimal point from the number in the numerator position.

• Place a 1 in front of the zeros in the denominator position.

• Convert to a mixed number and/or reduce to lowest terms if necessary.

Converting fractions to Converting fractions to decimalsdecimalsTo convert a fraction to a

decimal, divide the numerator of the fraction by the denominator

Lesson SummaryLesson SummaryThis lesson explains the types of

fractions and the calculations involving fractions. Calculation using fractions will be easier if you know how to simplify and convert fractions to decimals, and vice versa